Towards a Spectroscopically Towards a Spectroscopically Flexible Water Dimer Potential Flexible Water Dimer Potential

Energy SurfaceEnergy Surface

Ross E. A. KellyRoss E. A. Kelly, and Jonathan Tennyson, and Jonathan TennysonDepartment of Physics & AstronomyDepartment of Physics & Astronomy

University College LondonUniversity College London

Gerrit C. Groenenboom and Ad van der Avoird Gerrit C. Groenenboom and Ad van der Avoird Theoretical Chemistry, Institute for Molecules and Theoretical Chemistry, Institute for Molecules and

Materials, Materials, Radboud University, Nijmegen.Radboud University, Nijmegen.

Imperial College, December 2008

OutlineOutline

I. MotivationsI. Motivations II. The Water DimerII. The Water Dimer III. Vibration-Rotation TunnellingIII. Vibration-Rotation Tunnelling IV. Dimer PotentialsIV. Dimer Potentials V. Theoretical MethodV. Theoretical Method VI. VRT StatesVI. VRT States VII. Monomer Band OriginsVII. Monomer Band Origins VIII. Monomer Corrected SurfaceVIII. Monomer Corrected Surface IX. Conclusions & Further WorkIX. Conclusions & Further Work

I. MotivationsI. Motivations to understand to understand water dimer absorption water dimer absorption

throughout visible and IR region in the throughout visible and IR region in the atmosphere.atmosphere.

To create a To create a high accuracy water dimer high accuracy water dimer spectraspectra in agreement with in agreement with experimentsexperiments..

To create a To create a linelistlinelist of all possible of all possible water water dimer transitionsdimer transitions..

• To get all Vibration Rotation Energy Levels To get all Vibration Rotation Energy Levels Calculations require:Calculations require:

1. Some theoretical methodology for solving 1. Some theoretical methodology for solving the Hamiltonianthe Hamiltonian 2. High accuracy Potential Energy Surface2. High accuracy Potential Energy Surface

Preferably fully flexible (12D)Preferably fully flexible (12D)

•4 O-H distances4 O-H distances•2 H-O-H Angles2 H-O-H Angles•O-O distanceO-O distance•5 Euler Angles5 Euler Angles

II. Water DimerII. Water Dimer

Extremely Complex LandscapeExtremely Complex Landscape

X. Huang, B. J. Braams, J. M. Bowman, J. Phys. Chem. A 110, 445 (2006).

II. Water DimerII. Water Dimer

Complicated further by tunnelling effects!Complicated further by tunnelling effects! Tunnelling between eqiulavent states in the PES is Tunnelling between eqiulavent states in the PES is

feasible!feasible! Acceptor Tunnelling:Acceptor Tunnelling:

No bond breaking hereNo bond breaking hereLowest tunnelling barrier Lowest tunnelling barrier

Also, by breaking the Hydrogen bond, other tunnelling Also, by breaking the Hydrogen bond, other tunnelling paths possible: paths possible: Donor-Acceptor interchangeDonor-Acceptor interchangeDonor Bifurcation TunnellingDonor Bifurcation Tunnelling

III. Vibration-Rotation TunnellingIII. Vibration-Rotation Tunnelling

Can be represented by Permutation-Inversion Group GCan be represented by Permutation-Inversion Group G1616..

1 1

1 1

5 5

5 5

2 2

2 2

6 6

6 6

6 6

6 6

5

5 5

5

4

4

4

4

3

3

3

3

3 3

3 3

4

4

4

4

1 1

1 1

2

2 2

2

Isomorphic to D4h

with Irreducible Elements:

A1

+, A2

+, A1

-, A2

-, B1

+, B2

+, B1

-, B2

-, E+, E-

-> Water Dimer Spectroscopic Labels

III. Labelling Water Dimer StatesIII. Labelling Water Dimer States

[1] R. Bukowski, K. Szalewicz, G. C. Groenenboom, A. van der Avoird, Science 315, p1249-1252 (2007).

[2] X. Huang, B. J. Braams, J. M. Bowman, J. Phys. Chem. A 110, 445 (2006).

[3] X. Huang, B. J. Braams, J. M. Bowman, R. E. A. Kelly, J. Tennyson, G. C. Groenenboom, A. van der Avoird, J. Chem. Phys. 128,

034312 (2008)

Benchmark:Benchmark:●6D6D CC-polCC-pol Potential [1] - Potential [1] - Rigid MonomersRigid Monomers

New (2) New (2) 12D PESs12D PESs by Huang, Braams & Bowman by Huang, Braams & Bowman [2,3][2,3]

●HBB0HBB0 [2] [2] ●and and HBBHBB [3] – [3] – NEW 12D PESNEW 12D PES

- All completely - All completely ab initioab initio- Good agreement with experiment- Good agreement with experiment

Many PES’s available!Many PES’s available!

IV. Dimer Potentials AvailableIV. Dimer Potentials Available

• 30 000 configurations. 30 000 configurations.

• Calculated at coupled-cluster, single and double and Calculated at coupled-cluster, single and double and

perturbative treatment of triple excitations method.perturbative treatment of triple excitations method.

• augmented, correlation consistent, polarized triple zeta augmented, correlation consistent, polarized triple zeta

basis set.basis set.

• Polynomial fit with 5227 coefficients.Polynomial fit with 5227 coefficients.

• However, compared to However, compared to CCpolCCpol potential (benchmark): potential (benchmark):● Lower relative grid coverage of the surface than Lower relative grid coverage of the surface than

benchmark 6D PES.benchmark 6D PES.● Not extrapolated to the complete basis set limit Not extrapolated to the complete basis set limit

(CBS)(CBS)● No bond functions in analytical fitNo bond functions in analytical fit● Dissociation less accurately describedDissociation less accurately described

12DIV. IV. HBBHBB PES for H PES for H

44OO22

[1] X. Huang, B. J. Braams, J. M. Bowman, R. E. A. Kelly, J. Tennyson, G. C. Groenenboom, A. van der Avoird, J. Chem. Phys. 128, 034312

(2008).

• Dissociation Energy = 1665.82 cmDissociation Energy = 1665.82 cm-1-1 / 1757.90 cm / 1757.90 cm-1-1

• Other tests? Other tests?

• Compare with Low temperature high-resolution Compare with Low temperature high-resolution

Tetrahertz Spectroscopy (prepared in supersonic Tetrahertz Spectroscopy (prepared in supersonic

molecular beams), around 5 K.molecular beams), around 5 K.

• How can this be done theoretically?How can this be done theoretically?

IV. IV. HBBHBB PES for H PES for H44OO22

Rigid monomer Hamiltonian [1]:

Only for the Intermolecular modes

Used for water dimer previously, detailed account [2]

Coupled product of Symmetric rotor functions (Wigner-D functions) for the Angular coordinates

Radial basis: sinc Discrete Variable Representation (DVR)

[1] G. Brocks, A. van der Avoird, B. T. Sutcliffe, J. Tennyson, Mol. Phys. 50, 1025 (1983).

[2] G. C. Groenenboom, et al., JCP 113, 6702 (2000).

V. Theoretical Method for VRT levelsV. Theoretical Method for VRT levels

VI. Ground State VRT states for HVI. Ground State VRT states for H44OO22

[1] X. Huang, B. J. Braams, J. M. Bowman, R. E. A. Kelly, J. Tennyson, G. C. Groenenboom, A. van der Avoird, J. Chem. Phys. 128, 034312

(2008).

Very good agreement with:

Ground State Tunnelling splittings Rotational Constants

Not so good agreement with:

Acceptor Tunnelling

Excellent agreement with:

Ground State Tunnelling splittings Rotational Constants

Not so good agreement with:

Acceptor Tunnelling

[1] X. Huang, B. J. Braams, J. M. Bowman, R. E. A. Kelly, J. Tennyson, G. C. Groenenboom, A. van der Avoird, J. Chem. Phys. 128, 034312

(2008).

VI. Ground State VRT for DVI. Ground State VRT for D44OO22

In cm-1

Red – ab initio potential Black – experimental

GS – ground state

DT – donor torsion

AW – acceptor wag

AT – acceptor twist

DT2 – donor torsion overtone

VI. More low level VRT States for HVI. More low level VRT States for H44OO22

In cm-1

Red – ab initio potential Black – experimental

GS – ground state

DT – donor torsion

AW – acceptor wag

AT – acceptor twist

DT2 – donor torsion overtone

VI. More low level VRT States for DVI. More low level VRT States for D44OO22

VII. Monomer Band OriginsVII. Monomer Band Origins New 12D Huang New 12D Huang et al.et al. PES seems to work well: PES seems to work well:

– for low-level dimer VRT statesfor low-level dimer VRT states How about for H2O monomer energy levels?How about for H2O monomer energy levels? Use DVR3D [1] for Water monomer levels:Use DVR3D [1] for Water monomer levels:

ExciteExciteFixFix100 bohr

1. J. Tennyson et al., Comp. Phys. Comm. 2004, 163, 85-116.

Comparison is not so good.Comparison is not so good.

VII. Monomer Band OriginsVII. Monomer Band Origins

Blue HBB dimerBlue HBB dimerGreen HBB0Green HBB0Red Shirin 2008.Red Shirin 2008.(Monomer).(Monomer).

VIII. Adding Monomer CorrectionVIII. Adding Monomer Correction

)],,(),,([)](2)()([),( 21212121 eeecorr VVVVVV qqqqqqqqq

Correction for monomer modes:Correction for monomer modes:

New Potential Expression:New Potential Expression:

),(),,(),,(),,( 21212121 qqqqrqqrqq corrcorr VVVV

Tests for PotentialTests for Potential Evaluation of the saddle points.Evaluation of the saddle points. Evaluation of the monomer & dimer VRT states.Evaluation of the monomer & dimer VRT states.

VIII. Monomer Corrected SurfaceVIII. Monomer Corrected SurfaceCharacteristicCharacteristic HBBHBB HBB+MCHBB+MC

DDee -1657.12-1657.12 -1665.82-1665.82

Point 2Point 2 198.47198.47 193.46193.46

Point 3Point 3 243.98243.98 241.09241.09

Point 4Point 4 340.60340.60 358.06358.06

Point 5Point 5 1178.921178.92 1181.761181.76

Point 6Point 6 588.19588.19 590.19590.19

Point 7Point 7 894.83894.83 898.27898.27

Not Particularly worse than HBB potential.

Still a very good Still a very good agreement with agreement with exp.exp.

Nothing is Nothing is changed changed significantly.significantly.

VIII. Ground VIII. Ground State VRT State VRT

levels for Hlevels for H44OO22

VIII. More VIII. More VRT States VRT States for HBB+MCfor HBB+MC

surfacesurface

Again, Again, agreement is agreement is not not significantly significantly worse.worse.

IX. Conclusions & Further WorkIX. Conclusions & Further Work

Introduction of monomer correction makes PES Introduction of monomer correction makes PES more transferable for spectroscopic purposes.more transferable for spectroscopic purposes.

Little effect on dimer characteristics.Little effect on dimer characteristics. Monomer band origins significantly improved.Monomer band origins significantly improved. We are working towards a model which We are working towards a model which

incorporates monomer excitations into the dimer incorporates monomer excitations into the dimer states, so spectra can be produced.states, so spectra can be produced.